Page 63 - Math Genius C4

E:\Working\Orange_Education\Math_Genius_4\Open_Files\Chap-03
\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

4. Grouping Property: The product of three numbers does not change when we 2. Match the following multiplications with their properties.
change the grouping of the numbers. Column A Column B

Example: 20 × (6 × 5) = 20 × 30 = 600 (a) 3 × (4 × 6) = (3 × 4) × 6 (i) Distributive property of multiplication
(20 × 6) × 5 = 120 × 5 = 600 Same (b) 3 × 6 = 18 = 6 × 3 (ii) Multiplicative property of 1

So, 20 × (6 × 5) = (20 × 6) × 5. (c) 4 × (50 + 3) = 4 × 50 + 4 × 3 (iii) Order property of multiplication
The grouping property of multiplication is also known as the Associative Property of (d) 16 × 0 = 0 (iv) Grouping property of multiplication

multiplication. (e) 24 × 1 = 24 or 1 × 24 = 24 (v) Multiplicative property of 0
Distributive property of Multiplication

Rohan went to the stationery shop with his friend Kartik. Both of them bought a pencil estiMating tHe proDuct
each worth `5 and an eraser each worth `3. How much money did they spend altogether? We have already learned about rounding off numbers and finding the estimated sum and
Rohan calculated the amount as: difference of numbers. The same concept can be used to find the estimated product.

Total amount for two pencils and two erasers = 2 × `5 + 2 × `3 To estimate a product, we round off the multiplicand and the multiplier to the
= `(10 + 6) = `16 nearest ten, hundred or thousand, whichever is required. Then, multiply the rounded

Kartik used another way to calculate the total amount as: numbers to get the estimated product.
Cost of one pair of a pencil and an eraser = `5 + `3 Example 1: Estimate the product 38 × 44.
So, total amount for two pencils and two erasers = 2 × (`5 + `3) = 2 × `8 = `16 Solution: th H t O th H t O
Is the same amount of money obtained in each case? (Yes) 3 8 4 0 Rounded up to the nearest ten

Hence, we can say 2 × (5 + 3) = (2 × 5) + (2 × 3) × 4 4 × 4 0 Rounded down to the nearest ten
This is called the distributive property of 1 6 0 0 Estimated product

multiplication over addition. We say that Think Tank Critical Thinking Actual product = 38 × 44 = 1672
multiplication distributes over addition. Fill in the blanks. Example 2: Estimate the product 516 × 393 to the nearest (a) tens (b) hundreds.
1. 5 × 8 tens = _________.
Thus, the product of a number multiplied 2. 250 × 4 × 4 =_________. Solution: (a)
by the sum of two numbers is the same as 3. The number of zeros in the product th H t O L tth th H t O
of 1001 × 10 is _______.
the sum of the products of that number 4. The cost of one book is `180. The 5 1 6 5 2 0 Rounded up to the nearest ten
with the two numbers separately. cost of 100 such books is _________. × 3 9 3 × 3 9 0 Rounded down to the nearest ten
2 0 2 8 0 0 Estimated product

practice time 3e (b) th H t O L tth th H t O

1. Fill in the blanks. 5 1 6 5 0 0 Rounded down to the nearest hundred
4 0 0
(a) 457 × 0 = _____ (b) 761 × _____ = 761 (c) _____ × 1 = 278 × 3 9 3 × 2 0 0 0 0 0 Rounded up to the nearest hundred
Estimated product
(d) 321 × 1 = _____ (e) 3241 × _____ = 0 (f) 48 × 165 = 165 × _____ Actual product = 516 × 393 = 202788
(g) 432 × 522 = _____ × 432 (h) 169 × _____ = 215 × 169 From the above results, we see that rounding off to the nearest tens produces a

(i) 12 × (16 × 19) = (12 × _____) × 19 closer approximation of the exact product than rounding off to the nearest hundreds.
(j) 62 × ( _____ × 49) = (62 × 93) × 49 However, 520 × 390 involves more calculations than 500 × 400.

(k) 27 × (9 + 15) = (27 × 9) + (27 × _____) Teacher’s Discuss with students that, like the distributive property of multiplication over addition, we can also use the

(l) 102 × (100 + 58) = (102 × _____ ) + (102 × 58) Tip distributive property over subtraction, like: (200 – 3) × 43 = 200 × 43 − 3 × 43 = 8600 – 129 = 8471 which is
the same as the product of 197 (= 200 – 3) and 43.
Mathematics-4 61